The concept FilteredComplex describes the requirements for a type to implement a filtered cell complex, from which one can compute persistent homology via a model of the concept PersistentHomology. More...

Public Types
typedef unspecified	Simplex_handle
	Handle to specify a simplex.

typedef unspecified	Filtration_value
	Type for the value of the filtration function. More...

typedef unspecified	Indexing_tag
	Specifies the nature of the indexing scheme. More...

typedef unspecified	Boundary_simplex_iterator
	Iterator on the simplices belonging to the boundary of a simplex. More...

typedef unspecified	Boundary_simplex_range
	Range giving access to the simplices in the boundary of a simplex. More...

typedef unspecified	Filtration_simplex_iterator
	Iterator over all simplices of the complex in the order of the indexing scheme. More...

typedef unspecified	Filtration_simplex_range
	Range over the simplices of the complex in the order of the filtration. More...

Public Member Functions
Simplex_handle	null_simplex ()
	Returns a Simplex_handle that is different from all simplex handles of the simplices.

size_t	num_simplices ()
	Returns the number of simplices in the complex. More...

int	dimension (Simplex_handle sh)
	Returns the dimension of a simplex.

Filtration_value	filtration (Simplex_handle sh)
	Returns the filtration value of a simplex. More...

Simplex_handle	simplex (size_t idx)
	Returns the simplex that has index idx in the filtration. More...

Boundary_simplex_range	boundary_simplex_range (Simplex_handle sh)
	Returns a range giving access to all simplices of the boundary of a simplex, i.e. the set of codimension 1 subsimplices of the Simplex. More...

Filtration_simplex_range	filtration_simplex_range ()
	Returns a range over the simplices of the complex in the order of the filtration. More...

Map interface
Conceptually a `std::unordered_map<Simplex_handle,std::size_t>`.
typedef unspecified	Simplex_key
	Data stored for each simplex. More...

Simplex_key	null_key ()
	Returns a constant dummy number that is either negative, or at least as large as `num_simplices()`. Suggested value: -1.

Simplex_key	key (Simplex_handle sh)
	Returns the number stored for a simplex by `assign_key`. More...

void	assign_key (Simplex_handle sh, Simplex_key n)
	Store a number for a simplex, which can later be retrieved with `key(sh)`. More...

Detailed Description

The concept FilteredComplex describes the requirements for a type to implement a filtered cell complex, from which one can compute persistent homology via a model of the concept PersistentHomology.

Member Typedef Documentation

◆ Boundary_simplex_iterator

typedef unspecified FilteredComplex::Boundary_simplex_iterator

Iterator on the simplices belonging to the boundary of a simplex.

value_type must be 'Simplex_handle'.

◆ Boundary_simplex_range

typedef unspecified FilteredComplex::Boundary_simplex_range

Range giving access to the simplices in the boundary of a simplex.

.begin() and .end() return type Boundary_simplex_iterator.

◆ Filtration_simplex_iterator

typedef unspecified FilteredComplex::Filtration_simplex_iterator

Iterator over all simplices of the complex in the order of the indexing scheme.

'value_type' must be 'Simplex_handle'.

◆ Filtration_simplex_range

typedef unspecified FilteredComplex::Filtration_simplex_range

Range over the simplices of the complex in the order of the filtration.

.begin() and .end() return type Filtration_simplex_iterator.

◆ Filtration_value

typedef unspecified FilteredComplex::Filtration_value

Type for the value of the filtration function.

Must be comparable with <.

◆ Indexing_tag

typedef unspecified FilteredComplex::Indexing_tag

Specifies the nature of the indexing scheme.

is model of IndexingTag.

◆ Simplex_key

typedef unspecified FilteredComplex::Simplex_key

Data stored for each simplex.

Must be an integer type.

Member Function Documentation

◆ assign_key()

void FilteredComplex::assign_key	(	Simplex_handle	sh,
		Simplex_key	n
	)

Store a number for a simplex, which can later be retrieved with key(sh).

This is never called on null_simplex().

◆ boundary_simplex_range()

Boundary_simplex_range FilteredComplex::boundary_simplex_range ( Simplex_handle sh )

Returns a range giving access to all simplices of the boundary of a simplex, i.e. the set of codimension 1 subsimplices of the Simplex.

If the simplex is \([v_0, \cdots ,v_d]\), with canonical orientation induced by \( v_0 < \cdots < v_d \), the iterator enumerates the simplices of the boundary in the order: \([v_0,\cdots,\widehat{v_i},\cdots,v_d]\) for \(i\) from 0 to d

We note that the alternate sum of the simplices given by the iterator gives the chains corresponding to the boundary of the simplex.

◆ filtration()

Filtration_value FilteredComplex::filtration ( Simplex_handle sh )

Returns the filtration value of a simplex.

If sh is null_simplex(), returns the maximal value of the filtration function on the complex.

◆ filtration_simplex_range()

Filtration_simplex_range FilteredComplex::filtration_simplex_range ( )

Returns a range over the simplices of the complex in the order of the filtration.

.begin() and .end() return type Filtration_simplex_iterator.

◆ key()

Simplex_key FilteredComplex::key ( Simplex_handle sh )

Returns the number stored for a simplex by assign_key.

This is never called on null_simplex().

◆ num_simplices()

size_t FilteredComplex::num_simplices ( )

Returns the number of simplices in the complex.

Does not count the empty simplex.

◆ simplex()

Simplex_handle FilteredComplex::simplex ( size_t idx )

Returns the simplex that has index idx in the filtration.

This is only called on valid indices.

The documentation for this struct was generated from the following file:

concept/Persistent_cohomology/FilteredComplex.h

Public Types

Public Member Functions

Map interface